Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812746 | C2 | semidirect |
| 2. #20295841 | C2 | semidirect |
| 3. #20295837 | C2 | semidirect |
| 4. #20295824 | C2 | semidirect |
| 5. C2×#16812729 | C2 | semidirect |
| 6. #20295793 | C2 | semidirect |
| 7. #585×C109 | C2 | semidirect |
| 9. #16812746 | C22 | semidirect |
| 10. C2×#13182029 | C22 | semidirect |
| 12. C22×Dic218 | C22 | semidirect |
| 14. #16812730 | C22 | semidirect |
| 15. #16812729 | C22 | semidirect |
| 16. #16812729 | C22 | semidirect |
| 17. #16812725 | C22 | semidirect |
| 18. #16812724 | C22 | semidirect |
| 19. #16812719 | C22 | semidirect |
| 20. C2×#13182019 | C22 | semidirect |
| 21. C2×#13182017 | C22 | semidirect |
| 22. #16812706 | C22 | semidirect |
| 23. C2×#13182013 | C22 | semidirect |
| 25. 2−1+4×C109 | C22 | semidirect |
| 27. H(5,𝔽2)×C109 | C22 | semidirect |
| 113. C109 | #3586 | semidirect |
| 114. #585 | D109 | semidirect |
| 124. 2−1+4 | C2×D109 | semidirect |
| 126. H(5,𝔽2) | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812746 | 2 |
| #20295841 | 2 |
| #20295837 | 2 |
| #20295824 | 2 |
| C2×#16812729 | 2 |
| #20295793 | 2 |
| #585×C109 | 2 |
| #3586 | 109 |